I don't think your going to find much contiguous long distance singletrack stuff with current beta and totally clear trails. Most of it will be exploratory riding/hiking.
But, if your into that I would checkout the Whitefish Divide to Swan Crest Alpine Trail No.7. This is doable if you keep your milage expectations low. Also a nice resupply in Whitefish. An article about the Whitefish Divide from 09:
http://missoulanews.bigskypress.com/missoula/top-of-the-world/Content?oid=1228876 Or, a loop out of Salmon. Maybe heading to Panther Creek then Divide Trail 106 > Lost Horse Pass > CDT > Salmon. Salmon trail info:
http://www.ridesalmon.com/#!salmon-trails/ca4p. Very small resupply opportunities near Shoup. You could always put in a few road miles to Wisdom for a decent resupply.
Both of these would probably take around 10 days.